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C5×#70761 #14281981

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#70761

Splittings

FittingC3×C5×#431 ⋊ C2
HallC3×C5 ⋊ #1484
SylowC3 ⋊ C5×#1484

Subgroups

subgroupG/H
centerC2×C4×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#431C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5477C2
cosocleC3×C42C23×C5
hypercenterC5×#431D3
hypocenterC3C5×#1484
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C5×#431

524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7,8)(9,11,13,12)(10,15,16,14)(17,20,22,21)(18,23,19,24);(7,8)(10,14)(11,12)(15,16)(17,19)(18,22)(20,24)(21,23);(9,10)(11,15)(12,14)(13,16)(17,18,21,24,22,19,20,23)

Conjugacy classes & character table

390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7679);